A Challenge of Numbers describes the circumstances and issues centered on people in the mathematical sciences, principally students and teachers at U.S. colleges and universities. A healthy flow of mathematical talent is crucial not only to the future of U.S. mathematics but also as a keystone supporting a technological workforce. Trends in the mathematical sciences' most valuable resource--its people--are presented narratively, graphically, and numerically as an information base for policymakers and for those interested in the people in this not very visible, but critical profession.